We can finally appeal to Corollary 3.1 from [1]}, which states that
if \(X_1, \hdots , X_d\)  are i.i.d. Weibull random variables with tail parameter
\(\theta \) , then for all \(x \geqslant d K_{\theta }\)  we have
\( \operatornamewithlimits{\mathbb {P}}\left( \left|\sum _{j=1}^{d} X_j \right|\geqslant x \right)\leqslant \exp \left( - \left( \frac{x}{K_{\theta } d} \right)^{1/\theta } \right)\) 
